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The matrix-t distribution and its applications in predictive inference

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  • Kibria, B.M. Golam

Abstract

The predictive distributions of the future responses and regression matrix under the multivariate elliptically contoured distributions are derived using structural approach. The predictive distributions are obtained as matrix-t which are identical to those obtained under matrix normal and matrix-t distributions. This gives inference robustness with respect to departures from the reference case of independent sampling from the matrix normal or dependent but uncorrelated sampling from matrix-t distributions. Some successful applications of matrix-t distribution in the field of spatial prediction have been addressed.

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  • Kibria, B.M. Golam, 2006. "The matrix-t distribution and its applications in predictive inference," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 785-795, March.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:3:p:785-795
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    References listed on IDEAS

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    1. Kibria, B. M. Golam & Haq, M. Safiul, 1999. "Predictive Inference for the Elliptical Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 235-249, February.
    2. Kim, Hyoung-Moon & Mallick, Bani K., 2003. "A note on Bayesian spatial prediction using the elliptical distribution," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 271-276, September.
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    10. Kibria B.M.G. & Sun L. & Zidek J. V. & Le N. D., 2002. "Bayesian Spatial Prediction of Random Space-Time Fields With Application to Mapping PM2.5 Exposure," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 112-124, March.
    11. Loschi, Rosangela H. & Iglesias, Pilar L. & Arellano-Valle, Reinaldo B., 2003. "Predictivistic characterizations of multivariate student-t models," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 10-23, April.
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    Cited by:

    1. Dong, Xiaoyu & Mathew, Thomas, 2015. "Central tolerance regions and reference regions for multivariate normal populations," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 50-60.
    2. Liu, Jin Shan & Ip, Wai Cheung & Wong, Heung, 2009. "Predictive inference for singular multivariate elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1440-1446, August.
    3. Kozubowski, Tomasz J. & Mazur, Stepan & Podgorski, Krysztof, 2022. "Matrix Variate Generalized Laplace Distributions," Working Papers 2022:7, Örebro University, School of Business.

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